Co-H-structures on equivariant Moore spaces

Arkowitz, Martin; Golasiński, Marek

Fundamenta Mathematicae, Tome 144 (1994), p. 59-67 / Harvested from The Polish Digital Mathematics Library

Résumé

Let G be a finite group, $𝕆_{G}$ the category of canonical orbits of G and $A : 𝕆_{G} \to 𝔸$ b a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A,n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dim X < 2n - 1. If dim X = 2n-1, then the set of comultiplications of X is in one-one correspondence with $E x t^{n - 1} (A, A \otimes A)$ . Then the case $G = ℤ_{p^{k}}$ leads to an example of infinitely many G-homotopically distinct G-maps $φ_{i} : X \to Y$ such that $φ_{i}^{H}$ , $φ_{j}^{H} : X^{H} \to Y^{H}$ are homotopic for all i,j and all subgroups H ⊆ G.

Publié le : 1994-01-01

Zbl 0827.55006

EUDML-ID : urn:eudml:doc:212051

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     author = {Martin Arkowitz and Marek Golasi\'nski},
     title = {Co-H-structures on equivariant Moore spaces},
     journal = {Fundamenta Mathematicae},
     volume = {144},
     year = {1994},
     pages = {59-67},
     zbl = {0827.55006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv146i1p59bwm}
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Arkowitz, Martin; Golasiński, Marek. Co-H-structures on equivariant Moore spaces. Fundamenta Mathematicae, Tome 144 (1994) pp. 59-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv146i1p59bwm/

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